Given:

Partial floor framing for Rm A$110$ at the College of Engineering is provided in Figure $1.$ The floor framing consists

of one$-$way concrete joists spaced at $3^{\text{'}}-0^{\text{'}\text{'}}$ centers. The concrete joists have a clear span of ${35}^{\text{'}}-0^{\text{'}\text{'}}$ between

concrete girders.

Figure $1$ Partial floor framing for Rm A$110$

A section through the joists is shown in Figure $2.$ The thickness of the concrete floor slab is $\frac{41}{2^{.It}}$ is reinforced

with #$4$ bars spaced at $6$ o$.$c$.$ in the direction parallel with the concrete joists. The bottom of each joist is

reinforced with a #$9$ bar. The distance between adjacent joist webs is $30".$ The side of each joist is tapered at a

slope of $1$ and $12.$

Figure $2.$ Section through concrete joist framing

All concrete joists are constructed monolithically with the concrete slab and girders. For this reason, the joists are

continuous span members and have both negative and positive bending moments. The maximum negative

moment occurs at the face of each girder$-$joist connection, and the maximum positive moment occurs at

midspan. Instead of completing a structural analysis using influence diagrams to find these moments, ACl allows

analysis using the ACI coefficients in Table $6\mathrm{.}5\mathrm{.}2.$ To find the maximum moment, multiply the ACl coefficient $Cm$

by the uniform floor load and the square of the clear span where $=C{m}^{*}$ wu $l{n}^2.$ ACl coefficients for the

concrete floor joists are shown in Figure $3.$

Figure $3.$ ACI load coefficients for concrete floor joists in Rm $110$

Required:

Part A

Assume $3,000$ psi concrete and Grade $60$ steel. Find the design flexural strength of the concrete joists for

positive and negative bending $($Hint: In regions of negative bending, the distance $d$ to the reinforcing steel will

be from the bottom of the joist to the steel in the slab. Recall that all concrete below the neutral axis is assumed

to be cracked. The joist taper and steel located at the bottom of the web may be ignored for the flexural

analysis in negative bending regions.$)$

Part $B{?}_{(})$

In addition to the self$-$weight of the floor framing system, there is a superimposed dead load of $15psf$ for

mechanical ducts, electrical wiring, and ceiling loads. Determine the maximum uniform floor live load $LL($psf$)$ at

the service level that can be carried by the joists.

PLEASE SOLVE BOTH PARTS